For humanbeings to be twenty years old is still being at a tender age, whereas for institutions it sounds as if it were already the age of maturity. What is it for PME?
In an attempt to answer this question, I came back to the
introduction by Efraim Fishbein to the synthesis of our activities
that we published in 1990 under the title "Mathematics and Cognition"
(ICMI Study series, Cambridge University Press). Fishbein reminded us
the history of PME which genesis has its roots in a lecture from
Begle in 1969, and he emphasised the essential move which represented
the focus on the psychological complexity of mathematics as a content
to be learned. Aknowledging the development of research on
"psychological problems inspired by the school reality" (ibid. p.5),
Fishbein called for a more important effort on discussing the
theoretical framework of the field and shaping its specific
methodology. It was obvious to him that "mathematics education raises
its own psychological problems, which a professional psychologist
would never encounter in his own area" (ibid. p.10), and that for
this purpose we have to coin new concepts, to design new
methodologies, to develop a new epistemology in order to discuss the
validity of the statements we make as a result of our research. On
this respect PME has made a huge contribution over the past decade.
The Washington ICMI meeting organised by Jeremy Kilpatrick and Anka
Sierpinska in 1994 has clearly witnessed it. A majority of the
contribution originated in PME activities and PME members were the
most active group.
Nevertheless, the original challenge of Begle to
"turn mathematics education into an experimental science" has in my
opinion been very partially taken. The main reason is the legitimate
initial focus on the learner as such. I see this focus as a
consequence of the awaking of mathematicians to the fact that
problems of learning mathematics cannot be understood only from
inside the mathematics. Psychology, as a professional body was the
only one to be able to understand this call and to join
mathematicians in an effort to unfold the complexity of mathematics
from a learning perspective. PME has undertaken this work in an
enthousiastic maner, stimulating exchanges and discussions in a very
open way, rejecting elitism to the benefit of the growth of a
collective awareness of the necessity of a cognitive approach to
mathematics education, visiting the world from the North to the
South, the East to the West and inviting everyone to join the
international effort. But the original focus may now be obstacle to
an evolution which the original intention would not lead to reject.
Psychology is only part of the relevant approaches to the problems
raised by mathematics learning and teaching, and for example one must
be able to take teaching processes as an object of study as such, as
well as the epistemology of mathematics from a teaching/learning
perspective. These are not problems of psychology. Studying the
learning of mathematics within institutions like school is studying
learning and the object of learning under constraints which deserve a
specific problématique.
Actually, Fishbein in his introduction reminded us
that Freudenthal, in 1955, "insisted on the necessity of promoting
scientific research, including psychological considerations, to
respond to problems of mathematics education" (ibid. p.2). Psychology
was part of the project, it was not all the project and I would claim
again that PME itself, as a matter of fact, is nowaday beyond a
psychological approach to mathematics education.
It may now be time to move from and International
Group for the Psychology of Mathematics Education, to an
International Research Group on Teaching/Learning Mathematics. In
such a move we may be obliged to make clearer the specificity of our
research domain and of its links to mathematics, we may have to make
a special effort to be more rigorous, we may have to question what
allows us to pretend that we are contributing to the development of a
scientific body of knowledge. This move may be the price to turn the
twenties and to head for the forties, the time when life begins.
Grenoble, 6 May 1996
Nicolas Balacheff